Ringworld
The world is actually neither a disc or a sphere. It is a ring! There are m cities there, conveniently called 0, 1, 2, ..., m - 1, and arranged on the ring in the natural order: first 0, then 1, then 2, ..., then m - 1, and then again 0 (as the world is a ring, remember?). You are given a collection of contiguous ranges of cities. Each of them starts at some city x, and contains also cities x + 1, x + 2, ..., y - 1, y, for some city y. Note that the range can wrap around, for instance if m = 5, then [3, 4, 0] is a valid range, and so are [1], [2, 3, 4] or even [3, 4, 0, 1, 2].
Your task is to choose a single city inside each range so that no city is chosen twice for two different ranges.
Input
The first line contains the number of test cases t (1 ≤ t ≤ 20). Each test case consists of a number of lines. The first line contains two integers m (1 ≤ m ≤ 10^9
) and n (1 ≤ n ≤ 10^5
) denoting the number of cities and the number of requests, respectively. The next n lines define the ranges: the i-th row contains two integers x[i]
, y[i]
(0 ≤ x[i]
, y[i]
< m) describing the i-th range [x[i]
, x[i+1]
mod m, ..., y[i]
].
Output
For each test case, output one line containing YES if it is possible to assign a unique city to each request, and NO otherwise.